Thunder point guard Russell Westbrook added 31 points and six assists. Forward Serge Ibaka had a double-double with 11 points and 14 rebounds.
“Obviously, Kevin had a phenomenal game, but I thought Serge's two offensive rebounds down the stretch were a big part of the win,” Brooks said.
OKC won despite shooting just 41.1 percent from the floor and 30.0 percent from 3-point range.
The Mavs forced overtime by winning the fourth quarter 33-24 as the Thunder misfired at 31.6 percent from the field in the final period, which included Durant going 2 for 11.
“We won the game by shooting 41 percent because we got key stops when we needed it,” Brooks said. “Sometimes when your shot doesn't fall, you have to find a way to attack the basket and will yourself to get opportunities, and he did that tonight and got opportunities at the free-throw line.
“He's an amazing player.”
Dallas reserve guard Vince Carter, who frequently excels against the Thunder, had a season-high 29 points, while shooting 10 for 17 from the field and 4 for 8 from 3-point range.
His final attempt was a missed 3-pointer from the right wing at the final buzzer that could have sent the game into double-overtime.
Dirk Nowitzki missed 10 of his first 11 shots and finished 5 for 19 with 18 points.
The Thunder plays at Denver on Sunday at 7 p.m. Because of Friday's overtime effort, Brooks canceled Saturday's scheduled practice.